Supercapacitor electrodes consist of complex nanoporous structures in carbonaceous and non-carbonaceous materials causing alteration of electric double layer (EDL) structure and response. We develop a modular theory for DC-bias dependent electrochemical impedance spectroscopy (EIS) for EDL in the heterogeneous bimodal porous electrode, viz. arbitrary mesopores with embedded heterogeneous micropores. Theory accounts for the compact- and diffuse-EDL dynamics along with charge transfer kinetics of pseudocapacitance. The influence of applied DC-bias on various phenomenological components is accounted through a heuristic approach. This is achieved by using the potential and concentration dependent diffuse layer thickness for unsymmetrical electrolytes, charge transfer resistance, and electric field dependent dielectric constant. The generic nature of theory is further highlighted by extending it for the composite porous electrode materials. The theoretical response shows that increasing the magnitude of DC-bias enhances the characteristic ion relaxation rates therefore, increases the rate capability of supercapacitors. The electrode morphological parameters, viz. mesopore size, micropore size, micropore length, and the pore surface heterogeneity, can effectively tune the capacitance and charging-discharging rates therefore, influence the performance of supercapacitors. Finally, our theory explains the experimental EIS data for hierarchical sodium gluconate and graphdiyne porous electrodes.
